This serves as the main page for the Euler-Bernoulli Beam MATH 447 Project 1. Links to the problem description (PDF) and code used to generate the solutions below (.zip) may be obtained from the buttons above. This project sets out to investigate a fundamental model for material flex when stress is applied. Our specific project involves a 2 meter beam subjected to a variety of forces. We begin with the simple "diving board problem" and finish with a clamped-clamped model. While we set out to solve our equation systems to get a result, we also compare our solutions to the theoretical correct solutions graphically. We may reference variables throughout the postings.
A list of the values we used is as follows:
Problem 1: Basic initialization of the matrix shown on page 104 of the description PDF for \(n=10\).
Problem 2: Plot of solution obtained from Problem 1 against the theoretical correct solution \( (\frac{f}{24EI})x^2(x^2-4Lx+6L^2) \).
Problem 3: A rehash of Problem 1 for values of \(n=10 \cdot 2^k \) for \( k=1,...,11 \).
Problem 4: Theoretical exercise for finding the solution after adding a sinusoidal pile \( s(x) = -pg\sin(\frac{\pi}{L}x) \).
Problem 5: Variation of Problem 3 with the added sinusoidal load from Problem 4.
Problem 6: After removing the sinusoidal load, we add a 70 kg diver to the beam on the last 20 cm.
Problem 7: To finish up, we clamp the free end of the beam and add a sinusoidal load.